Q40. - Algebra 1

Question

FINANCIAL LITERACY The current price of each share of a technology company is $135. If this represents a 16.2% increase over the past year, what was the price per share a year ago?

Step-by-Step Solution

Answer

The price of each share a year ago was $116.18.

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

Step 2. Example of the percentage change.

For example, if a person has 25 dollars and he gets 3 more dollars and now has 28 dollars, its percentage increase is calculated as shown:

 $\begin{array}{l}\text{Increase }=28-25=3\\ \%\text{ change = r, then}\\ \frac{3}{25}=\frac{r}{100}\\ r=\frac{3}{25}\times 100\\ =12\%\end{array}$

Step 3. Find the percentage change.

We are given that the Current share price of a technology company is $135. And that it is a 16.2% increase over the past year.

 $\frac{\text{Change}}{\text{Original amount}}=\frac{r}{100}$

If we let x represent the price of each share a year ago, we can find it as follows:

$\begin{array}{l}\text{Change :135-x}\\ \frac{135-x}{\text{x}}=\frac{16.2}{100}\\ 100\left(135-x\right)=16.2x\\ 13500-100x=16.2x\\ 13500=16.2x+100x\\ 13500=116.2x\\ x=\frac{13500}{116.2}\\ x=116.18\end{array}$

Thus, the price of each share a year ago was $116.18.